Nonnegative Sparse Matrix Factorization
Description
nmfsc
: R implementation of nmfsc
.
Usage
1 
Arguments
X 
the data matrix. 
p 
number of hidden factors = number of biclusters; default = 5. 
cyc 
maximal number of iterations; default = 100. 
sL 
sparseness loadings; default = 0.6. 
sZ 
sparseness factors; default = 0.6. 
Details
Nonnegative Matrix Factorization represents positive matrix X by positive matrices L and Z that are sparse.
Objective for reconstruction is Euclidean distance and sparseness constraints.
Essentially the model is the sum of outer products of vectors:
X = ∑_{i=1}^{p} λ_i z_i^T
where the number of summands p is the number of biclusters. The matrix factorization is
X = L Z
Here λ_i are from R^n, z_i from R^l, L from R^{n \times p}, Z from R^{p \times l}, and X from R^{n \times l}.
If the nonzero components of the sparse vectors are grouped together then the outer product results in a matrix with a nonzero block and zeros elsewhere.
The model selection is performed by a constraint optimization according to Hoyer, 2004. The Euclidean distance (the Frobenius norm) is minimized subject to sparseness and nonnegativity constraints.
Model selection is done by gradient descent on the Euclidean objective and thereafter projection of single vectors of L and single vectors of Z to fulfill the sparseness and nonnegativity constraints.
The projection minimize the Euclidean distance to the original vector given an l_1norm and an l_2norm and enforcing nonnegativity.
The projection is a convex quadratic problem which is solved iteratively where at each iteration at least one component is set to zero. Instead of the l_1norm a sparseness measurement is used which relates the l_1norm to the l_2norm.
The code is implemented in R.
Value

object of the class 
Author(s)
Sepp Hochreiter
References
Patrik O. Hoyer, ‘Nonnegative Matrix Factorization with Sparseness Constraints’, Journal of Machine Learning Research 5:14571469, 2004.
D. D. Lee and H. S. Seung, ‘Algorithms for nonnegative matrix factorization’, In Advances in Neural Information Processing Systems 13, 556562, 2001.
See Also
fabia
,
fabias
,
fabiap
,
fabi
,
fabiasp
,
mfsc
,
nmfdiv
,
nmfeu
,
nmfsc
,
extractPlot
,
extractBic
,
plotBicluster
,
Factorization
,
projFuncPos
,
projFunc
,
estimateMode
,
makeFabiaData
,
makeFabiaDataBlocks
,
makeFabiaDataPos
,
makeFabiaDataBlocksPos
,
matrixImagePlot
,
fabiaDemo
,
fabiaVersion
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36  #
# TEST
#
dat < makeFabiaDataBlocks(n = 100,l= 50,p = 3,f1 = 5,f2 = 5,
of1 = 5,of2 = 10,sd_noise = 3.0,sd_z_noise = 0.2,mean_z = 2.0,
sd_z = 1.0,sd_l_noise = 0.2,mean_l = 3.0,sd_l = 1.0)
X < dat[[1]]
Y < dat[[2]]
X < abs(X)
resEx < nmfsc(X,3,30,0.6,0.6)
## Not run:
#
# DEMO
#
dat < makeFabiaDataBlocks(n = 1000,l= 100,p = 10,f1 = 5,f2 = 5,
of1 = 5,of2 = 10,sd_noise = 3.0,sd_z_noise = 0.2,mean_z = 2.0,
sd_z = 1.0,sd_l_noise = 0.2,mean_l = 3.0,sd_l = 1.0)
X < dat[[1]]
Y < dat[[2]]
X < abs(X)
resToy < nmfsc(X,13,100,0.6,0.6)
extractPlot(resToy,ti="NMFSC",Y=Y)
## End(Not run)
